Given `veca=xhati+yhatj+2hatk,vecb=hati-hatj+hatk , vecc=hati+2hatj, veca botvecb,veca.vecc=4` then find the value of `[(veca, vecb, vecc)]`.

Options

A. `[vecavecbvecc]^(2)=|veca|`
B. `[vecavecbvecc]=|veca|`
C. `[vecavecbvecc]=0`
D. `[vecavecbvecc]=0`

Answer

d

Explanation

`veca bot vecb Rightarrow x -y + 2=0`
`veca ,vecb = 4 Rightarrow x+2y= 4 `
Solving we get x =0 , y =2
` Rightarrow veca = 2hatj + 2hatk`
`Rightarrow [veca vecb vecc] =|{:(0,2,2),(1,-1,1),(1,2,0):}|=8=|veca|^(2)`